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Weighted composition operators /Kwok, Ka-keung. January 1993 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 47-49).
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Singular integral operators associated to approximately homogeneous curvesWeinberg, David A. January 1980 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 29).
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Control of holomorphic semigroups generated by a class of spectral operatorsRebarber, Richard. January 1984 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison,1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 182-184).
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Realization theory of infinite-dimensional linear systemsYamamoto, Yutaka, January 1978 (has links)
Thesis--University of Florida. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 80-83).
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Prime ideals in differential operator rings and crossed productsChin, William. January 1985 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1985. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.
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Relative eigenvalue problems for ordinary differential operatorsHughes, Charles Edward, January 1970 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.
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Self-adjoint matrix equations on time scalesBuchholz, Bobbi January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed July 9, 2007). PDF text: 96 p. UMI publication number: AAT 3252832. Includes bibliographical references. Also available in microfilm and microfiche formats.
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Properties of eigenvalues of singular second order elliptic operatorsWelsh, K. Wayne January 1970 (has links)
This thesis investigates the properties of the L₂-eigenvalues of singular, elliptic, second order operators, primarily the operator L defined by
[formula omitted].
Here the "potential function", V(x), is such that [formula omitted] is a norm on [formula omitted] being the usual norm in the Sobolev space W¹̕²(G) and [formula omitted] is the completion of [formula omitted] in the metric from this norm, identified with a subset L₂(G) ; Δ is the Laplacian and G is an arbitrary open domain of E[superscript n] .
Several sufficient conditions are given on V and on G in order that L have spectrum satisfying [formula omitted] , for some real number [formula omitted] denote the spectrum and point spectrum of L , respectively).
The properties of these lower eigenvalues are investigated
by examining the eigenvalues of a coercive bilinear form corresponding to the operator. Such a form B , having domain [symbol omitted] , say, is defined to have eigenvalueλє¢ with corresponding eigenfunction [symbols omitted] if B[u,f] = λ (u,f) for all f є [symbol omitted] . Variational properties are discussed in detail; In particular, a condition is given which ensures that the numbers sup inf B[u,u] (the sup and inf being over appropriate
sets involving [symbol omitted] and n ) are eigenvalues of B .
These properties are applied to L to generalize the well-known classical property (G bounded) of monotonic dependence of the eigenvalues on the underlying domain G : G [symbol omitted] G* implies [formula omitted] for corresponding eigenvalues, with strict inclusion implying strict inequality. A few miscellaneous
properties of the eigenvalues and eigenfunctions then follow from this dependence. / Science, Faculty of / Mathematics, Department of / Graduate
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Some problems in differential operators (essential self-adjointness)Keller, R. Godfrey January 1977 (has links)
We consider a formally self-adjoint elliptic differential operator in IR<sup>n</sup>, denoted by τ. T<sub>0</sub> and T are operators given by τ with specific domains. We determine conditions under which T<sub>0</sub> is essentially self-adjoint, introducing the topic by means of a brief historical survey of some results in this field. In Part I, we consider an operator of order 4, and in Part II, we generalise the results obtained there to ones for an operator of order 2m. Thus, the two parts run parallel. In Chapter 1, we determine the domain of T<sub>0</sub>*, denoted by D(T<sub>0</sub>*), where T<sub>0</sub>* denotes the adjoint of T<sub>0</sub>, and introduce operators <u>T</u><sub>0</sub> and <u>T</u> which are modifications of T<sub>0</sub> and T. In Chapter 2, we use a theorem of Schechter to give conditions under which <u>T</u><sub>0</sub> is essentially self-adjoint. Working with the operator <u>T</u>, in Chapter 3 ve show that we can approximate functions u in D(T<sub>0</sub>*) by a particular sequence of test-functions, which enables us to derive an identity involving u, Tu and the coefficient functions of the operator concerned. In Chapter 4, we determine an upper bound for the integral of a function involving a derivative of u in D(T<sub>0</sub>*) whose order is half the order of the operator concerned, and we use the identity from the previous chapter to reformulate this upper bound. In Chapter 5, we give conditions which are sufficient for the essential self-adjointness of T<sub>0</sub>. In the main theorem itself, the major step is the derivation of the integral of the function involving the particular derivative of u in D(T<sub>0</sub>*) whose order is half the order of the operator concerned, referred to above, itself as a term of an upper bound of an integral we wish to estimate. Hence, we can employ the upper bound from Chapter 4. This "sandwiching" technique is basic to the approach we have adopted. We conclude with a brief discussion of the operators we considered, and restate the examples of operators which we showed to be essentially self-adjoint.
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Compact Operators of Sequence SpacesWang, Wei-Hong 19 June 2001 (has links)
In this thesis, we study weighted composition operatorsT(xn)=(£fnX£m(n)) between sequence spaces(c0,c,l1,lp), and more precisely, the sufficient and necessary condition that they are compact. First,we obtain some results of weighted composition operators beingcompact, weakly compact and completely continuous on c0 spaces. Then, we extend then to c,l1,and lp(1<p<¡Û) spaces. Finally, we obtain the condition that an operator from c0, c or lp into c0, c, or lq is compact, weakly compact or completely continuous.
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